Satellite constellations

ABSTRACT

A constellation of satellites includes a first plurality of satellites orbiting at a first inclination, wherein the first plurality of satellites are each in a discrete planar orbit to form a first snake of satellites, the first snake of satellites including adjacent satellites in adjacent orbits having adjacent RAAN (Right Ascension of the Ascending Node).

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application claims the benefit of U.S. Provisional PatentApplication Nos. 62/465,110 and 62/465,064, both filed Feb. 28, 2017,the disclosures of which are hereby expressly incorporated by referenceherein in their entirety.

BACKGROUND

Communication satellites receive and transmit radio signals from and tothe surface of Earth for the purpose of providing communicationservices. In conventional satellite technology, only a few locations onEarth were in view of a satellite at any given time to transmit and/orreceive signals to and/or from a satellite. In more modern satellitetechnology, it is desirable for every place on Earth be providedcommunication services at all times, a capability which may be referredto as universal or global coverage. In addition to global coverage, somelocations on Earth, such as densely populated areas, require morecommunication capacity than others.

For global coverage, communication systems may employ non-geostationarysatellites. Geostationary satellites orbit the equator with an orbitalperiod of exactly one day (flying at an altitude of approximately 35,786km above mean sea level). Therefore, geostationary satellites remain inthe same area of the sky as viewed from a specific location on Earth. Incontrast, non-geostationary satellites typically operate in low- ormid-Earth orbit and do not remain stationary relative to a specificlocation on Earth.

Satellite constellations are needed with improved global coverage andimproved communication capacity. Embodiments of the present disclosureare directed to fulfilling these need and other needs.

SUMMARY

This summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This summary is not intended to identify key features ofthe claimed subject matter, nor is it intended to be used as an aid indetermining the scope of the claimed subject matter.

In one embodiment of the present disclosure, a constellation ofsatellites is provided. The constellation of satellites includes a firstplurality of satellites orbiting at a first inclination, wherein thefirst plurality of satellites are each in a discrete planar orbit toform a first snake of satellites, the first snake of satellitesincluding adjacent satellites in adjacent orbits having adjacent RAAN(Right Ascension of the Ascending Node).

In another embodiment of the present disclosure, a constellation ofsatellites is provided. The constellation of satellites includes: afirst plurality of satellites orbiting at a first inclination, whereinthe first plurality of satellites are each in a discrete planar orbit toform a first snake of satellites, the first snake of satellitesincluding adjacent satellites in adjacent orbits having adjacent RAAN(Right Ascension of the Ascending Node), wherein the stagger betweensatellites in the first snake of satellites is substantially constant;and a second plurality of satellites orbiting at a second inclination,wherein the second inclination is different from the first inclination,wherein the second plurality of satellites are each in a differentplanar orbit to form a second snake of satellites, the second snake ofsatellites including adjacent satellites in adjacent orbits havingadjacent RAAN, wherein the stagger between satellites in the secondsnake of satellites is substantially constant.

In any of the embodiments described herein, by selective placement ofadjacent satellites in relative argument of latitude and RAAN, thevirtual ascending node of the constellation snake may have acontrollable regression rate.

In any of the embodiments described herein, the stagger betweensatellites in the first snake of satellites may be substantiallyconstant.

In any of the embodiments described herein, the snake may define aplurality of loops forming a continuous path.

In any of the embodiments described herein, the constellation ofsatellites may further include a second plurality of satellites orbitingat a second inclination, wherein the second inclination is differentfrom the first inclination, wherein the second plurality of satellitesare each in a different planar orbit to form a second snake ofsatellites, the second snake of satellites including adjacent satellitesin adjacent orbits having adjacent RAAN.

In any of the embodiments described herein, the stagger betweensatellites in the second snake of satellites may be substantiallyconstant.

In any of the embodiments described herein, wherein the first and secondsnakes may have a synchronized virtual RAAN rate such that theirascending nodes maintain constant spacing.

In any of the embodiments described herein, the first and second snakesmay provide fixed and interleaved ground coverage at the equator.

In any of the embodiments described herein, the first and second snakesmay provide fixed and overlapping ground coverage at the equator.

In any of the embodiments described herein, the first inclination may bein a range selected from the group consisting of between 30 degrees and60 degrees and between 40 degrees and 55 degrees.

In any of the embodiments described herein, the second inclination maybe in a range selected from the group consisting of between 30 degreesand 60 degrees and between 40 degrees and 55 degrees.

In any of the embodiments described herein, the first snake may be afirst repeating ground track.

In any of the embodiments described herein, the second snake may be asecond repeating ground track.

In any of the embodiments described herein, the first snake may be afirst drifting ground track.

In any of the embodiments described herein, the second snake may be asecond drifting ground track.

In any of the embodiments described herein, the satellites in the firstplurality of satellites may be located at an altitude range in spaceselected from the group consisting of between 200 km and 400 km, between300 km and 400 km, and between 330 km and 350 km from Earth.

In any of the embodiments described herein, the satellites in the secondplurality of satellites may be located at an altitude range in spaceselected from the group consisting of between 200 km and 400 km, between300 km and 400 km, and between 330 km and 350 km from Earth.

In any of the embodiments described herein, the satellites in the firstsnake and the satellites in the second snake may be within an altitudeof each other in a range of less than or equal to 200 km.

In any of the embodiments described herein, the satellite constellationmay further include a third plurality of satellites traveling at a thirdinclination, wherein the third inclination is different from the firstand second inclinations, wherein the third plurality of satellites areeach in a different planar orbit to form a third snake of satellites,the third snake of satellites including adjacent satellites in adjacentorbits having adjacent RAAN.

DESCRIPTION OF THE DRAWINGS

The foregoing aspects and many of the attendant advantages of thisdisclosure will become more readily appreciated as the same becomebetter understood by reference to the following detailed description,when taken in conjunction with the accompanying drawings, wherein:

FIGS. 1A and 1B are schematics of first and second satellite systemshaving different inclinations and similar altitudes resulting indrifting orbital planes in accordance with previously developedsatellite constellation technology.

FIG. 2A is a schematic of first and second satellite systems havingdifferent inclinations and different altitudes resulting in non-driftingorbital planes in accordance with previously developed satelliteconstellation technology.

FIG. 2B is a schematic describing the ascending node of an orbiting bodyin accordance with embodiments of the present disclosure.

FIG. 3A is a schematic comparing a satellite string in an orbital plane,and a satellite string with each satellite having a discrete orbit,ground-tracking string in accordance with embodiments of the presentdisclosure.

FIG. 3B is a schematic showing a plurality of satellite strings insynchronized ground-tracking strings with each satellite in each stringhaving a discrete orbit and all satellites and strings at the sameinclination in accordance with embodiments of the present disclosure.

FIG. 3C is a schematic showing a plurality of satellite strings insynchronized ground-tracking strings with each satellite in each stringhaving a discrete orbit and with the strings at two differentinclinations in accordance with embodiments of the present disclosure.

FIG. 4 is a schematic showing a plurality of satellite strings inrepeating ground-tracking strings with each satellite in each stringhaving a discrete orbit and with the strings at two differentinclinations (no drift) in accordance with embodiments of the presentdisclosure.

FIG. 5 is a schematic showing a plurality of satellite strings inground-tracking strings with each satellite in each string having adiscrete orbit and with the strings at two different inclinations (fixeddrift) in accordance with embodiments of the present disclosure.

FIG. 6 is a graph showing how altitude varies to maintain a fixed driftbetween a second satellite system having a different inclination in asynchronized ground track or a synchronized planar orbit in accordancewith embodiments of the present disclosure.

FIGS. 7A and 7B are close-up schematic views of equator crossings byindividual satellites in satellite strings in accordance withembodiments of the present disclosure are provided.

FIG. 8 is a close-up schematic view of equator crossings by individualsatellites in satellite strings showing longitude of ascending node(LAN) values in accordance with embodiments of the present disclosureare provided.

FIGS. 9-11 are directed to examples of ground coverage for varioussatellite constellations in accordance with embodiments of the presentdisclosure.

DETAILED DESCRIPTION

Embodiments of the present disclosure are directed to constellations ofsatellites having synchronized ground tracks, in contrast to traditionalsatellite constellations of “synchronized planes” with strings ofsatellites following each other in the same orbital planes. Inaccordance with one embodiment of the present disclosure, strings ofsatellites having synchronized ground tracks orbit the Earth in “wave”configurations, with each satellite in the string of satellites having adiscrete orbital plane. “Wave” configurations may also be referred toherein as “snake”, “string”, or “ground track” configurations.

For the purposes of global satellite coverage applications, for example,for global internet coverage, a large number of satellites are neededdefining a predictable grid of satellite coverage. If there are notenough satellites in a predictable grid, frequent service outages mayoccur. The design of the constellation of satellites to meet the needsof the communication application is a function of desired satellitealtitude and inclination pairing, antenna characteristics, and whetherthe ground tracks are repeating or non-repeating ground tracks, alldescribed in greater detail below.

While the concepts of the present disclosure are susceptible to variousmodifications and alternative forms, specific embodiments thereof havebeen shown by way of example in the drawings and will be describedherein in detail. It should be understood, however, that there is nointent to limit the concepts of the present disclosure to the particularforms disclosed, but on the contrary, the intention is to cover allmodifications, equivalents, and alternatives consistent with the presentdisclosure and the appended claims.

References in the specification to “one embodiment,” “an embodiment,”“an illustrative embodiment,” etc., indicate that the embodimentdescribed may include a particular feature, structure, orcharacteristic, but every embodiment may or may not necessarily includethat particular feature, structure, or characteristic. Moreover, suchphrases are not necessarily referring to the same embodiment. Further,when a particular feature, structure, or characteristic is described inconnection with an embodiment, it is submitted that it is within theknowledge of one skilled in the art to affect such feature, structure,or characteristic in connection with other embodiments whether or notexplicitly described. Additionally, it should be appreciated that itemsincluded in a list in the form of “at least one A, B, and C” can mean(A); (B); (C); (A and B); (B and C); (A and C); or (A, B, and C).Similarly, items listed in the form of “at least one of A, B, or C” canmean (A); (B); (C); (A and B); (B and C); (A and C); or (A, B, and C).

In the drawings, some structural or method features may be shown inspecific arrangements and/or orderings. However, it should beappreciated that such specific arrangements and/or orderings may not berequired. Rather, in some embodiments, such features may be arranged ina different manner and/or order than shown in the illustrative figures.Additionally, the inclusion of a structural or method feature in aparticular figure is not meant to imply that such feature is required inall embodiments and, in some embodiments, it may not be included or maybe combined with other features.

Many embodiments of the technology described herein may take the form ofcomputer- or controller-executable instructions, including routinesexecuted by a programmable computer or controller. Those skilled in therelevant art will appreciate that the technology can be practiced oncomputer/controller systems other than those shown and described above.The technology can be embodied in a special-purpose computer, controlleror data processor that is specifically programmed, configured orconstructed to perform one or more of the computer-executableinstructions described above. Accordingly, the terms “computer” and“controller” as generally used herein refer to any data processor andcan include Internet appliances and hand-held devices (includingpalm-top computers, wearable computers, cellular or mobile phones,multi-processor systems, processor-based or programmable consumerelectronics, network computers, mini computers and the like).Information handled by these computers can be presented at any suitabledisplay medium, including a CRT display or LCD.

Unsynchronized (Drifting) Orbital Planes

Referring to FIG. 1A, a constellation of satellites in accordance withpreviously developed technology is provided. The constellation showsfour satellite orbits in four different orbital planes, includingsatellites strings A, B, C, and D. For simplification in the illustratedembodiment, the satellite strings include one satellite. However, inaccordance with embodiments of the present disclosure, each satellitestring includes a plurality of satellites following each other in thepath of the orbital plane.

Satellite strings A, B, C, D are at similar altitudes, but at differentinclinations, inclinations angle A and inclination angle B. For example,string A is at an inclination α of about 55 degrees relative to theequator E and string B is at an inclination β of about 32 degreesrelative to the equator E. Satellite strings C and D mirror satellitestrings A and B.

The altitudes of the satellite strings are not exactly the same to avoidcollision of satellites in different systems, but they are within closerange of each other, such that altitude is a minimal factor in thedifferent operating characteristics of the first and second satellitestrings A and B. For example, satellite string A and satellite string Bmay be in an altitude range of a few kilometers, less than 200 km.

Referring to FIG. 1B, the two satellite strings A and B of FIG. 1A havedifferent westward drift rates in view of their different inclinations Aand B. Therefore, after a period of time, the second string ofsatellites B has drifted more westward than the first string ofsatellites A, as shown by drift differential ΔD. The drift differentialΔD between the first and second satellite strings A and B is undesirablebecause it adds uncertainty to the meshing between the two areas ofcoverage by the two satellite strings A and B. Meshing or interleavingbetween satellite strings is desirable in communication systems thatdepend on a known satellite constellation for predictable satellitecoverage.

As described in greater detail below, the meshing or interleavingbetween satellite strings may have a fixed drift between the satellitestrings (which is called a “synchronized ground track”) or the meshingbetween satellite strings may have no drift relative to the rotation ofthe Earth (which is called a “synchronized repeating ground track”because the strings of satellites always follow the same ground track onthe Earth with each rotation around the Earth). As described in greaterdetail below, embodiments of the present disclosure are directed tosatellite constellations having synchronized ground tracks or satelliteconstellations having synchronized repeating ground tracks.

The satellite constellations of the present disclosure are innon-geostationary orbits. A satellite in a geostationary orbit is at analtitude of approximately 35,786 km above mean sea level. Satelliteconstellations of the present disclosure are at lower altitudes. In oneembodiment of the present disclosure, the satellite constellation of thepresent disclosure is at an altitude of less than 10,000 km. In anotherembodiment, the satellite constellation of the present disclosure is ina low Earth orbit at an altitude of less than 2000 km. In anotherembodiment, the satellite constellation of the present disclosure is ina very low Earth orbit at an altitude of less than 500 km.

Synchronized (Fixed Drift) Orbital Planes

Referring to FIG. 2A, one solution for reducing the difference in driftrate between two satellite systems in accordance with previouslydeveloped technology is to fly the two satellite systems at twodifferent altitudes. See altitude h1 for satellite string A and altitudeh2 for satellite string B. The altitude difference between the twosatellite systems A and B can be fixed such that the precession of theright ascension of the ascending node (RAAN) is identical for thesatellites in either satellite orbital plane.

Referring to FIG. 2B, for a geocentric orbit of an object orbitingEarth, Earth's equatorial plane E is the reference plane and the FirstPoint of Aries γ (which is considered to be the celestial “PrimeMeridian”) is the origin of longitude. In an inertial frame with theEarth rotating, the longitude of the orbit is wherein the orbit crossesthe plane of reference measured from the reference direction γ, measuredeastwards (or, as seen from the north, counterclockwise) from the FirstPoint of Aries γ to the ascending node Ω, and is called the rightascension of the ascending node (RAAN). Two numbers orient the orbitalplane in space: inclination and RAAN.

As described in greater detail below with reference to FIG. 8, thelongitude of the ascending node (LAN) is measured relative to the PrimeMeridian (Greenwich Line), in the geographic coordinate system at whichlongitude is defined to be 0° dividing the Earth into the EasternHemisphere and the Western Hemisphere (in contrast to RAAN, which ismeasured relative to a celestial plane of reference).

Returning for FIG. 2A, string A may, for example, be at an inclination αof about 55 degrees relative to the equator E and an altitude ofapproximately 1150 km and string B may be at an inclination β of about32 degrees relative to the equator E and an altitude of approximately2040 km. Because the precession of the RAAN for the two satellitesystems is identical, the systems drift together in a locked drift suchthat they continue to mesh and be interleaved.

RAAN precession can be calculated using the following equation:

$\overset{.}{\Omega} = {{- \frac{3}{2}}{J_{2}\left( \frac{{Radius}_{Earth}}{p_{A}} \right)}^{2}n_{A}}$${\cos\; i_{A}} = {{- \frac{3}{2}}{J_{2}\left( \frac{{Radius}_{Earth}}{p_{B}} \right)}^{2}n_{B}\cos\; i_{B}}$$n = \sqrt{\frac{\mu}{a^{3}}}$ p = a(1 − e²)

Wherein Ω⋅ is RAAN precession, J2 is Earth's oblateness,

Radius

_Earth is the Earth's mean equatorial radius, i is the orbitinclination, a is the orbit semi-major axis, e is the orbiteccentricity, and μ is the Earth's gravitational parameter.

While a locked drift is desirable for satellite coverage, it may bedifficult to acquire government licenses needed to operate two orbitalsatellite strings in two different altitudes required for a lockeddrift. In addition, satellites configured to fly at altitudes that arewithin close altitude range (for example, within an altitude range ofless than about 200 km) can be designed with similar (if not the same)design characteristics. Satellites flying at vastly different altitudespresent design challenges due to differences in flying conditions.

Strings of Satellites with Each Satellite in Each String Having aDiscrete Orbit

Referring to FIG. 3A, in accordance with embodiments of the presentdisclosure, a first satellite string W making a loop is shown having a“wave” formation with each satellite in each string having a discreteorbit. The first satellite string W includes a plurality of satellitesS1, S2, S3, etc., following each other in a wave formation, wherein eachsatellite takes a separate and discrete orbital path around the Earth,as indicated by the dotted orbital paths of two of the satellites S2 andS13 in the satellite string W.

As seen in FIG. 3A, an orbital satellite string A is also shown forcomparison.

A loop in a string of satellites is defined by two simultaneouscrossings of the equator in the same crossing direction by a specificsatellite in the string of satellites. As seen in FIG. 3A, a specificsatellite S1 is crossing the equator E at an ascending node (from thesouthern hemisphere to the northern hemisphere) at a first time at t1. Aloop of the string of satellites is completed when satellite S1 crossesthe equator again at an ascending node (from the southern hemisphere tothe northern hemisphere) at a second time at t2. Of note, on theopposite side of the Earth, the satellite S1 will cross the equator fromthe opposite crossing direction at a descending node (from the northernhemisphere to the southern hemisphere), which defines a half loop.

Referring to FIG. 3B, a satellite string W at the same inclination α asprovided in FIG. 3A is shown. In FIG. 3A, the satellite string W travelsone loop in an inertial frame. However, in FIG. 3B, in a frame thatrotates with the Earth, the satellite string W travels multiple loops toform a continuous path around the Earth. A continuous path is formedwhen the first satellite in the sting of satellites repeats previousground track on the earth, thus forming a continuous path with the lastsatellite in the string of satellites.

As seen in FIG. 3B, each satellite in the satellite string W takes adiscrete orbital path around the Earth, as indicated by the arrowsextending from each of the satellites in the wave formation showing theinertial velocity of each satellite.

In the illustrated embodiment of FIG. 3B, the satellite string W makes13 loops around the Earth to form a continuous path. The inclination andnumber of loops in the satellite string W defining the path of thesatellite string W is application specific and is designed based on manyfactors including the altitude of the satellite string, semi-major axis,eccentricity of the satellite orbits, number of loops, and inclination.

The ground track is shared between satellites in the string W. However,the orbits of the satellites in the string W are not shared. Adjacentsatellites in the string are able to follow the same ground trackbecause the Earth rotates a little in the time two adjacent satellitesmove a certain distance. The satellites in the string are in differentorbits, meaning they “start” in different places, but by the time eachsatellite moves to a certain latitude, the Earth has rotated to put thesame point in the way of each satellite. Therefore, the satellites inthe string share a ground track and therefore have a synchronized groundtrack.

The path of the satellite string W can be designed to be a repeatingground or a non-repeating ground track, both of which are within thescope of the present disclosure. In a repeating ground track, the pathof the satellite string W is designed to align with the rotation of theEarth, such that after a set number of loops, the path of the satellitestring W repeats over the same locations on the Earth.

In a non-repeating ground track, the path of the satellite string Wdrifts eastward or westward relative to its previous path.

In accordance with embodiments of the present disclosure, the continuouspath of the satellite string W may be formed within less than 20 days,less than 15 days, less than 7 days, and less than 2 days. If thesatellite string W is configured for a repeating ground track, thecontinuous path will be aligned with the revolution of the Earth (whichis in one day). If the satellite string W is configured for anon-repeating ground track, the continuous path will not be aligned withthe revolution of the Earth.

The number of satellites in a satellite string W may vary in accordancewith embodiments of the present disclosure. In some embodiments, thesatellite string may include more than 10 satellites, more than 20satellites, and more than 30 satellites. In some embodiments, thesatellite string may include 10 to 300 satellites,

Referring to FIG. 3C, a plurality of interleaved satellite strings W_(A)and W_(B) at two different inclinations is provided. (W_(A) is atinclination α and W_(B) is at inclination β, with neither angle ofinclination show in FIG. 3C.) Details of interleaved satellite stringswill be discussed in greater detail below. In general, a lower number ofsatellites can be used in wave satellite strings and interleaved wavesatellite strings in accordance with embodiments of the presentdisclosure to achieve the same or better coverage achieved by orbitalsatellite strings. Exemplary satellite constellations are provided belowin Examples 1-3.

Synchronized (No Drift) Repeating Ground Tracks

Referring to FIG. 4, in a frame that rotates with the Earth, thesatellites in the first and second satellite strings X1 and Y1 are indiscrete orbits, each defining a “wave” formation with the two satellitestring X and Y having different inclinations. X1 is at inclination α andY1 is at inclination β, with neither angle of inclination show in FIG.4.)

In the illustrated embodiment, the first and second satellite strings X1and Y1 are repeating ground track systems. Therefore, the drift of thefirst and second satellite strings X1 and Y1 is designed to match theEarth's rotation rate. As a result, the Earth appears to stand stillrelative to the movement of the satellite strings X1 and Y1, thus givingthe appearance of no drift. Each satellite string X1 and Y1 is set up ina “wave” formation (as described with reference to FIG. 3A above) withcharacteristics such that the wave drifts west at the same rate as theEarth's rotation.

A repeating ground track is achieved by a certain number of loops in thestring of satellites based on the characteristics of the wave. In theillustrated embodiment of FIG. 4, both satellite strings X1 and Y1 havesimilar altitudes close to 1150 km and both satellite strings X1 and Y1run 13 loops until they repeat their ground track. The ground tracks aretherefore fixed, repeating paths on Earth. However, the number of loopscannot be altered to maintain this repeating ground track system ofsatellites at the same altitude. If a less dense or a more dense grid ofsatellite coverage is desired by changing the number of loops in thesystem tracks, the system will drift along the equator, as described ingreater detail below with reference to FIG. 5.

In accordance with embodiments of the present disclosure, the first andsecond satellite strings X1 and Y1 are repeating ground track systemsthat repeat their ground tracks when the continuous path of thesatellite strings X1 and Y1 are completed. Therefore, in someembodiments, the ground tracks may repeat within a time period of lessthan 20 days, less than 15 days, less than 7 days, and less than 2 days.

The two strings of satellites at different inclinations are synchronizedby using the following equations:

$\omega = {{{\overset{.}{\Omega}}_{A} + \frac{n_{A} + \left( {\overset{.}{M}}_{0} \right)_{A} + \left( \overset{.}{AoP} \right)_{A}}{\left( k_{revpday} \right)_{A}}} = {{\overset{.}{\Omega}}_{B} + \frac{n_{B} + \left( {\overset{.}{M}}_{0} \right)_{B} + \left( \overset{.}{AoP} \right)_{B}}{\left( k_{revpday} \right)_{B}}}}$${\overset{.}{M}}_{0} = {\frac{3}{4}{J_{2}\left( \frac{{Radius}_{Earth}}{p} \right)}^{2}n\sqrt{1 - e^{2}}\left( {2 - {3\left( {\sin\; i} \right)^{2}}} \right)}$$\overset{.}{AoP} = {\frac{3}{4}{J_{2}\left( \frac{{Radius}_{Earth}}{p} \right)}^{2}{n\left( {4 - {5\left( {\sin\; i} \right)^{2}}} \right)}}$$k_{revpday} = \frac{k_{{rev}\; 2{rep}}}{k_{{day}\; 2{rep}}}$

Where J2, n, e, i, p, and

Radius

_Earth are defined above, k_rev2rep is the number of equatorialcrossings, and k_day2rep is the exact number of nodal days it takes forthose crossings to occur.

A nodal day is defined as: 2π/(ω_E−Ω⋅), where ω_E is the Earth'srotation rate.

If value of ω is set equal to Earth's rotation rate ω_E, the resultingorbits will be repeat ground track orbits. The value of ω can also beset to other rotation rates besides ω_E.

Some embodiments of the present disclosure are directed tomultiple-inclination synchronization of satellite strings over a smallaltitude range (for example, within an altitude range of about 200 km).The satellite strings may have repeating ground tracks or non-repeatingground tracks.

Synchronized (Fixed Drift) Non-Repeating Ground Tracks

Referring to FIG. 5, in a frame that rotates with the Earth, thesatellites in the first and second satellite strings X2 and Y2 are indiscrete orbits, each defining a “wave” formation and each satellitestring X2 and Y2 having a different inclination, similar to thesatellite constellation seen above in FIG. 4.

Unlike the strings in FIG. 4 above, the strings X2 and Y2 in FIG. 5 arenot designed with the required number of loops to be repeating groundtrack systems. In contrast, the first and second strings X2 and Y2 drift(with synchronization or drift lock DL) eastward relative to the Earth'srotation rate. Each satellite string is set up in a “wave” formation (asdescribed with reference to FIG. 3A above), and the intersection of thetwo satellite strings X2 and Y2 drifts (with drift lock DL). In theillustrated embodiment of FIG. 5, the drift DL is shown as a eastwarddrift, but in other satellite constellations the drift may be westwardor eastward depending on the design of the system.

The advantage of such a system shown in FIG. 5 with a non-repeatingground track (as compared to the repeating ground track in FIG. 4) isthat the number of loops in the satellite strings X2 and Y2 can varywhile still maintaining drift lock DL between the first and secondsatellite strings X2 and Y2. For example, in the illustrate embodimentof FIG. 4 above, both satellite strings X1 and Y1 have similar altitudesclose to 1150 km and both satellite systems X1 and Y1 run 13 loops untilthe satellite strings X1 and Y1 repeat their ground track. In contrast,in the illustrated embodiment of FIG. 5, both satellite strings X2 andY2 have similar altitudes close to 1150 km and both satellite systems X2and Y2 run 7 loops, establishing a synchronized, but non-repeatingground track.

Because the satellite systems X2 and Y2 in FIG. 5 are synchronized todrift at the same rate with drift lock DL, the satellite coverage of thesatellite system X2 and Y2 remains meshed or interleaved. As describedabove, meshing or interleaving between satellite strings is desirable incommunication systems that depend on a known satellite constellation forpredictable satellite coverage.

Altitude Difference Needed for Synchronized Planes Versus SynchronizedGround Tracks

Referring to FIG. 6, a graph showing how altitude varies to maintain afixed drift between a second satellite system having a differentinclination in a synchronized ground track or in a synchronized planarorbit. The graph of FIG. 6 plots altitude (in km) versus inclination (indegrees). The orbit that is being synchronized in the graph for fixeddrift is arbitrarily set at about 345 km altitude and 53 degreeinclination.

The dotted line in FIG. 6 shows that many hundreds of kilometers ofaltitude difference are required to synchronize planar orbits even a fewdegrees apart in inclination.

The solid line in FIG. 6 shows that all inclinations from 0 to 180degrees for synchronized ground tracks can be matching in an altitudespan of about 200 km. Therefore, synchronized (fixed drift) groundtracks can be achieved within a small altitude span of about 200 km, forexample, a small altitude span within a single government-licensedaltitude band for orbiting satellite spacecraft.

Stagger for Satellites in a String

Referring to FIGS. 7A and 7B, close-up views of equator crossings byindividual satellites in a satellite string in accordance with oneembodiment of the present disclosure are provided. In FIG. 7A, onesatellite string A is shown at inclination A. In FIG. 7B, two satellitestrings A and B are shown at inclinations A and B.

Referring to FIG. 7A, satellite string A includes first and secondadjacent satellites A1 and A2 in adjacent orbits (see, e.g., adjacentorbits in FIG. 3A) having adjacent RAAN in accordance with embodimentsof the present disclosure. Although satellites A1 and A2 are in adjacentorbits and have adjacent RAAN, they have the same inclination α.

At a first time t1, satellite A1 crosses the equator at an ascendingnode (from the southern hemisphere to the northern hemisphere), andsatellite A2 is nearing the equator. At a second time t2, satellite A1again crosses the equator at an ascending node (from the southernhemisphere to the northern hemisphere), completing a loop around theEarth, and satellite A2 is again nearing the equator, also completing aloop around the Earth.

The longitudinal distance along the equator between adjacent ascendingnodes of the same satellite A1 across the equator (from the southernhemisphere to the northern hemisphere) is calculated by the followingequation:

$\frac{2{\pi\left( {\omega_{E} - {\overset{.}{\Omega}}_{A}} \right)}}{n_{A} + \left( {\overset{.}{M}}_{0} \right)_{A} + \left( \overset{.}{AoP} \right)_{A}}$

The stagger between adjacent satellites A1 and A2 in the same satellitestring A is the ratio between the difference in RANN between adjacentsatellites A1 and A2 divided by the difference in argument of latitudebetween adjacent satellites A1 and A2.Stagger=ΔΩ/Δ(v+ω)

In the above equation for stagger, Ω⋅ is RAAN, v is true anomaly, and ωis argument of periapsis. Argument of latitude is equally to the sum oftrue anomaly and argument of periapsis.

Stagger is illustrated in FIG. 3A as the relationship between the changein RAAN ΔΩ and the change in relative argument of latitude Δ(v+ω)between satellites in a wave satellite string W. The stagger value isthe same whether the satellites are adjacent each other or distancedfrom each other in the wave satellite string W. With a consistentstagger value between satellites in the satellite string, the satellitestring has a controllable regression rate or drift rate.

If the satellite string A is a repeating ground track system, then thedrift of the satellite string A is designed to match the Earth'srotation rate, as designed by the number of loops in the path of thesatellite string A for the specific altitude of the satellite string. Ina repeating ground track system in accordance with embodiments of thepresent disclosure, RAAN repeats after a predetermined number of loopsin the satellite path.

If the satellite string A is a non-repeating ground track system, thenthe drift of the satellite string A may vary from the Earth's rotationrate, as designed by the number of loops in the path of the satellitestring A for the specific altitude of the satellite string. In asynchronized constellation of two satellite strings, RAAN precession isin drift lock.

Referring to FIG. 7B, satellite string A includes first and secondadjacent satellites A1 and A2 in adjacent orbits having adjacent RAAN,and at the same inclination α.

In addition, satellite string B includes first and second adjacentsatellites B1 and B2 in adjacent orbits having adjacent RAAN, and at thesame inclination β (which is different from inclination α of satellitestring A).

At a first time t1, satellite A1 at inclination α crosses the equator atan ascending node (from the southern hemisphere to the northernhemisphere), and satellite A2 also at inclination α is nearing theequator. At the same time t1, satellite B1 at inclination β crosses theequator at an ascending node (from the southern hemisphere to thenorthern hemisphere), and satellite B2 also at inclination β is nearingthe equator.

At a second time t2, satellite A1 at inclination α again crosses theequator at an ascending node (from the southern hemisphere to thenorthern hemisphere), and satellite A2 also at inclination α is againnearing the equator. At the same time t2, satellite B1 at inclination βagain crosses the equator at an ascending node (from the southernhemisphere to the northern hemisphere), and satellite B2 also atinclination β is again nearing the equator.

The distance along the equator between adjacent crossings of samesatellite B1 across the equator between nodes (from the southernhemisphere to the northern hemisphere) is calculated by the followingequation:

$\frac{2{\pi\left( {\omega_{E} - {\overset{.}{\Omega}}_{B}} \right)}}{n_{B} + \left( {\overset{.}{M}}_{0} \right)_{B} + \left( \overset{.}{AoP} \right)_{B}}$

The relative argument of latitude drift Δ between A1 and B1 after A1 haddone exactly one loop is calculated by the following equation:

$\Delta = {\left( {{t\; 2} - {t\; 1}} \right)\left( {\frac{n_{B} + \left( {\overset{.}{M}}_{0} \right)_{B} + \left( \overset{.}{AoP} \right)_{B}}{\left( k_{revpday} \right)_{B}} - \frac{{n_{A}\left( {\overset{.}{M}}_{0} \right)}_{A} + \left( \overset{.}{AoP} \right)_{A}}{\left( k_{revpday} \right)_{A}}} \right)}$

Referring to FIG. 8, the longitude of the ascending node (LAN) ismeasured relative to the Prime Meridian (Greenwich Line), which in thegeographic coordinate system at which longitude is defined to be 0°dividing the Earth into the Eastern Hemisphere and the WesternHemisphere.

Like in FIG. 7B, the satellite string A in FIG. 8 includes first andsecond adjacent satellites A1 and A2 in adjacent orbits and at the sameinclination α. In addition, satellite string B includes first and secondadjacent satellites B1 and B2 in adjacent orbits and at the sameinclination β (which is different from inclination α of satellite stringA). LAN A1 and LAN A2 values and LAN B1 and LAN B2 values are shown.

Description of Claimed Embodiments

Embodiments of the present disclosure are directed to constellations ofsatellites having synchronized ground tracks, in contrast to thetraditional method of “synchronized planes”. In accordance with oneembodiment of the present disclosure, constellations of satelliteshaving synchronized ground tracks orbit the Earth in “snake”, “string”,or “ground track” configurations instead of following each other inorbital planes.

In a snake, the constellation of satellites includes a first pluralityof satellites at a first inclination, with each of the first pluralityof satellites in a different planar orbit. The snake of satellitesincludes adjacent satellites in adjacent orbits having adjacent RAAN(Right Ascension of the Ascending Node).

By selective placement of adjacent satellites in relative argument oflatitude and RAAN, the “virtual ascending node” of the constellationsnake has a controllable regression rate.

In embodiments of the present disclosure, the stagger between satellitesin the first snake of satellites is substantially constant.

In embodiments of the present disclosure, the snake defines a pluralityof loops forming a continuous path.

If a snake/ground track has N equatorial crossings before repeating,then the location of those crossings can be identified on a map with Nlongitudes of the ascending node. Arbitrarily picking any of thesecrossings as Crossing 1, and setting its longitude of the ascending nodeas the “virtual ascending node” of the snake/ground track, we canidentify the orientation of the complete snake/ground track by thissingle “virtual ascending node”. This virtual ascending node can eitherbe fixed for all time (=a repeat ground track orbit), or it can drifteast/west over time (=a drifting ground track). Whether it is fixed, orwhether it drifts and at what rate, can be controlled through carefulspecification of the exact orbital parameters (semi-major axis,inclination, and eccentricity) of the snake/ground track.

In another embodiment of the present disclosure, the constellation ofsatellites includes a second plurality of satellites orbiting at asecond inclination, wherein the second inclination is different from thefirst inclination. The satellites of the second plurality of satellitesare each in a different planar orbit to form a second snake ofsatellites. The second snake of satellites includes adjacent satellitesin adjacent orbits having adjacent RAAN.

In embodiments of the present disclosure, the stagger between satellitesin the second snake of satellites is substantially constant.

In accordance with embodiments of the present disclosure, the first andsecond snakes have a synchronized virtual RAAN rate such that theirascending nodes maintain constant spacing.

In one embodiment, the first and second snakes provide fixed andinterleaved ground coverage at the equator. In another embodiment, thefirst and second snakes provide fixed and overlapping ground coverage atthe equator.

For suitable applications, such as satellite global internet coverage,the first inclination may be in range selected from the group consistingof between 30 degrees and 60 degrees and between 40 degrees and 55degrees. Likewise, the second inclination may be in a range selectedfrom the group consisting of between 30 degrees and 60 degrees andbetween 40 degrees and 55 degrees. However, other inclination ranges arewithin the scope of the present disclosure, with inclination dependingon the technical application for the satellite constellation.

In embodiments of the present disclosure, the RAAN rate of the snakes iscontrollable. The first and second snakes may be in repeating groundtracks or in drifting ground tracks.

In one embodiment of the present disclosure, the satellites in the firstor second plurality of satellites may be located at an altitude range inspace selected from the group consisting of between 300 km and 400 kmand between 330 km and 350 km from Earth. Constellations of satelliteshaving synchronized ground tracks may be located in other altituderanges depending on the technical application for the satelliteconstellation.

In one embodiment, the satellites in the first snake and the satellitesin the second snake may be within an altitude of each other in a rangeof less than or equal to 200 km.

In another embodiment of the present disclosure, the satelliteconstellation may include a third plurality of satellites traveling at athird inclination. The third inclination is different from the first andsecond inclinations. The satellites of the third plurality of satellitesare each in a different planar orbit to form a third snake ofsatellites, the third snake of satellites including adjacent satellitesin adjacent orbits having adjacent RAAN.

In accordance with embodiments of the present disclosure, the satelliteconstellation may include any number of pluralities of satellites indifferent applications, depending on the technical application for thesatellite constellation.

Example 1 One Inclination, One Ground Track

Referring to FIG. 9, an exemplary contour plot of satellitecommunication coverage is provided. The contour plot shows the meannumber of satellites in view. The ground track is a repeating groundtrack with 31 satellite revolutions every 2 days. The number ofsatellites is 2549 at altitude 345.6 km. The inclination of thesatellite string X1 is at 53.0. The spacecraft antenna nadir angle is40.5 degrees, and the user terminal minimum elevation angle is 46.8degrees.

The lines of the contour plot show the ground track of the satellites inthe satellite string X1. The ground tracks may be repeating ornon-repeating (i.e., moving slowly across the surface of the Earth,either East or West). The contour plot shows communication coverageincreases where the ground tracks cross. The contour plot shows nocommunication coverage at a certain distance from the ground tracks.

Example 2 Two Inclinations, Two Ground Tracks

Referring to FIG. 10, an exemplary contour plot of satellitecommunication coverage is provided. The contour plot shows the meannumber of satellites in view. The first and second ground tracks eachinclude 31 satellite revolutions every 2 days. The number of satellitesin the two ground tracks is 5026 at altitudes 345.6 and 340.8. Theinclinations of the satellite strings X1 and Y1 are at 53.0 and 48.0.The spacecraft antenna nadir angle is 40.5 degrees, and the userterminal minimum elevation angle is 46.8 degrees.

The lines of the contour plot show the first and second ground tracks ofthe satellites in the satellite strings X1 and Y1. The ground tracks maybe repeating or non-repeating (i.e., moving slowly across the surface ofthe Earth, either East or West). The contour plot shows communicationcoverage increases compared to the communication coverage in EXAMPLE 1as a result of the addition of the second ground track at a secondinclination.

Example 3 Three Inclinations, Three Ground Tracks

Referring to FIG. 11, an exemplary contour plot of satellitecommunication coverage is provided. The contour plot shows the meannumber of satellites in view. The first, second, and third ground trackseach include 31 satellite revolutions every 2 days. The number ofsatellites in the three ground tracks is 7518 at altitudes 345.6, 340.8,and 335.9 kms. The inclinations of the satellite strings X1, Y1, and Z1are at 53.0, 48.0, and 42.0 degrees. The spacecraft antenna nadir angleis 40.5 degrees, and the user terminal minimum elevation angle is 46.8degrees.

The lines of the contour plot show the first, second, and third groundtracks of the satellites in the satellite strings X1, Y1, and Z1. Theground tracks may be repeating or non-repeating (i.e., moving slowlyacross the surface of the Earth, either East or West). The contour plotshows significantly increased communication coverage increases comparedto the communication coverage in EXAMPLES 1 and 2 as a result of theaddition of the third ground track at a third inclination.

While illustrative embodiments have been illustrated and described, itwill be appreciated that various changes can be made therein withoutdeparting from the spirit and scope of the disclosure.

The invention claimed is:
 1. A constellation of satellites, comprising:a first plurality of satellites orbiting at a first inclination, whereinthe first plurality of satellites are each in a discrete planar orbit toform a first snake of satellites, the first snake of satellitesincluding adjacent satellites in adjacent orbits having adjacent RAAN(Right Ascension of the Ascending Node), wherein the snake defines aplurality of loops forming a continuous path.
 2. A constellation ofsatellites of claim 1, wherein by selective placement of adjacentsatellites in relative argument of latitude and RAAN, the virtualascending node of the constellation snake has a controllable regressionrate.
 3. A constellation of satellites of claim 1, wherein the staggerbetween satellites in the first snake of satellites is substantiallyconstant.
 4. The constellation of satellites of claim 1, furthercomprising a second plurality of satellites orbiting at a secondinclination, wherein the second inclination is different from the firstinclination, wherein the second plurality of satellites are each in adifferent planar orbit to form a second snake of satellites, the secondsnake of satellites including adjacent satellites in adjacent orbitshaving adjacent RAAN.
 5. The constellation of satellites of claim 4,wherein the stagger between satellites in the second snake of satellitesis substantially constant.
 6. The constellation of satellites of claim4, wherein the first and second snakes have a synchronized virtual RAANrate such that their ascending nodes maintain constant spacing.
 7. Theconstellation of satellites of claim 4, wherein the first and secondsnakes provide fixed and interleaved ground coverage at the equator. 8.The constellation of satellites of claim 4, wherein the first and secondsnakes provide fixed and overlapping ground coverage at the equator. 9.The constellation of satellites of claim 1, wherein the firstinclination is in a range selected from the group consisting of between30 degrees and 60 degrees and between 40 degrees and 55 degrees.
 10. Theconstellation of satellites of claim 4, wherein the second inclinationis in a range selected from the group consisting of between 30 degreesand 60 degrees and between 40 degrees and 55 degrees.
 11. Theconstellation of satellites of claim 1, wherein the first snake is afirst repeating ground track.
 12. The constellation of satellites ofclaim 4, wherein the second snake is a second repeating ground track.13. The constellation of satellites of claim 1, wherein the first snakeis a first drifting ground track.
 14. The constellation of satellites ofclaim 4, wherein the second snake is a second drifting ground track. 15.The constellation of satellites of claim 1, wherein the satellites inthe first plurality of satellites are located at an altitude range inspace selected from the group consisting of between 200 km and 400 km,between 300 km and 400 km, and between 330 km and 350 km from Earth. 16.The constellation of satellites of claim 4, wherein the satellites inthe second plurality of satellites are located at an altitude range inspace selected from the group consisting of between 200 km and 400 km,between 300 km and 400 km, and between 330 km and 350 km from Earth. 17.The constellation of satellites of claim 1, wherein the satellites inthe first snake and the satellites in the second snake are within analtitude of each other in a range of less than or equal to 200 km. 18.The constellation of satellites of claim 1, further comprising a thirdplurality of satellites traveling at a third inclination, wherein thethird inclination is different from the first inclination and a secondinclination of a second plurality of satellites, wherein the thirdplurality of satellites are each in a different planar orbit to form athird snake of satellites, the third snake of satellites includingadjacent satellites in adjacent orbits having adjacent RAAN.
 19. Aconstellation of satellites, comprising: a first plurality of satellitesorbiting at a first inclination, wherein the first plurality ofsatellites are each in a discrete planar orbit to form a first snake ofsatellites, the first snake of satellites including adjacent satellitesin adjacent orbits having adjacent RAAN (Right Ascension of theAscending Node), wherein the stagger between satellites in the firstsnake of satellites is substantially constant; and a second plurality ofsatellites orbiting at a second inclination, wherein the secondinclination is different from the first inclination, wherein the secondplurality of satellites are each in a different planar orbit to form asecond snake of satellites, the second snake of satellites includingadjacent satellites in adjacent orbits having adjacent RAAN, wherein thestagger between satellites in the second snake of satellites issubstantially constant.